A KAM Theorem for Hamiltonian Partial Differential Equations with Unbounded Perturbations

被引：119

作者：

Liu, Jianjun ^{[1
]}

Yuan, Xiaoping

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2011年 / 307卷 / 03期

基金：

中国博士后科学基金;

关键词：

GLOBAL WELL-POSEDNESS; SCHRODINGER-OPERATORS;

D O I：

10.1007/s00220-011-1353-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We establish an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, which could be applied to a large class of Hamiltonian PDEs containing the derivative partial derivative(x) in the perturbation. Especially, in this range of application lie a class of derivative nonlinear Schrodinger equations with Dirichlet boundary conditions and perturbed Benjamin-Ono equation with periodic boundary conditions, so KAM tori and thus quasi-periodic solutions are obtained for them.

引用

页码：629 / 673

页数：45

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